arxiv: 2604.08444 · v1 · submitted 2026-04-09 · ✦ hep-ph

Recognition: unknown

LFV decays in a 3-4-1 model with minimal inverse seesaw neutrinos

N.H.T. Nha , L.T. Hue , L.T.T. Phuong , T.T. Hong

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification ✦ hep-ph

keywords 3-4-1 modelminimal inverse seesawlepton flavor violationmuon g-2 anomalytau to mu gammacharged Higgsneutrino masses

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The pith

A 3-4-1 model with minimal inverse seesaw neutrinos generates strong correlations between the electron and muon g-2 anomalies and lepton flavor violating decay rates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies an extended 3-4-1 gauge model that adds a new singly charged Higgs boson and implements the minimal inverse seesaw mechanism for generating neutrino masses. This construction simultaneously explains the observed anomalies in the electron and muon anomalous magnetic moments while producing lepton flavor violating decays of charged leptons, the Standard Model-like Higgs boson, and the Z boson. The central result is that the model creates tight correlations among these quantities. In particular, the present experimental upper limit on the branching fraction of tau to muon gamma decay restricts the allowed deviation in the muon g-2 to at most 10 to the minus 9 from the Standard Model value, remaining compatible with the one-sigma experimental range.

Core claim

The model predicts strong correlations among the (g-2)e,μ anomalies and the LFV decay rates of charged leptons, the SM-like Higgs, and the Z boson. The current upper bound on Br(τ → μγ) imposes a stringent constraint compatible with the 1σ experimental range of (g-2)μ, corresponding to a maximal deviation of 10^{-9} from the SM prediction. The forthcoming experimental sensitivity to Br(τ → μγ) will reduce this deviation to 5×10^{-10}.

What carries the argument

The 3-4-1 gauge symmetry extended by a minimal inverse seesaw neutrino sector and a new singly charged Higgs boson, whose Yukawa couplings and mass parameters generate the correlations between the magnetic moment anomalies and the flavor-violating processes.

If this is right

The existing upper limit on Br(τ → μγ) caps the maximum allowed deviation in (g-2)μ at 10^{-9}.
Improved sensitivity to Br(τ → μγ) will further restrict the possible (g-2)μ shift to 5×10^{-10}.
The same parameter choices that fit the g-2 anomalies also determine the rates for LFV decays of the Higgs and Z bosons.
All current experimental data on these observables can be accommodated simultaneously within the model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Independent searches for the new singly charged Higgs at colliders could test the same parameter region that controls the g-2 and LFV correlations.
The required neutrino mass matrices may imply specific patterns in oscillation data or neutrinoless double-beta decay rates.
If the g-2 anomalies are confirmed at the predicted level, the model would forecast measurable LFV signals at next-generation flavor experiments.

Load-bearing premise

The Yukawa couplings and mass parameters in the minimal inverse seesaw sector can be adjusted to fit the g-2 anomalies while keeping all lepton flavor violating rates below current experimental limits and consistent with observed neutrino masses.

What would settle it

A future measurement showing Br(τ → μγ) below the current bound together with a (g-2)μ deviation larger than 10^{-9} from the Standard Model value would contradict the correlations required by the model.

Figures

Figures reproduced from arXiv: 2604.08444 by L.T. Hue, L.T.T. Phuong, N.H.T. Nha, T.T. Hong.

**Figure 2.** Figure 2: FIG. 2: One-loop Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Feynman diagrams for one-loop contributions to the decay amplitudes [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: The correlations between ∆ [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: The correlations between ∆ [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: The relationship between decay rates of cLFV, LFV [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗

read the original abstract

We investigate an extended 3-4-1 model consisting of a new singly charged Higgs boson, implementing the minimal inverse seesaw mechanism to accommodate the large values of the $(g-2)_{e,\mu}$ anomalies as well as the lepton-flavor-violating decay rates of charged leptons, the Standard Model-like Higgs boson, and the $Z$ boson, all consistent with current experimental data. Unlike the previously studied 3-4-1 realization, the model considered here predicts strong correlations among these observables that can be tested in future experiments. In particular, the current upper bound on Br$(\tau \to \mu \gamma)$ imposes a stringent constraint compatible with the $1\sigma$ experimental range of $(g-2)_{\mu}$, corresponding to a maximal deviation of $10^{-9}$ from the SM prediction. The forthcoming experimental sensitivity to Br$(\tau \to \mu\gamma)$ will reduce this deviation to $5\times 10^{-10}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This 3-4-1 model with minimal inverse seesaw ties g-2 anomalies to LFV rates via correlations absent in prior versions, with tau-mu-gamma bounds capping the deviation at 10^{-9}.

read the letter

The punchline is that this 3-4-1 model with the minimal inverse seesaw creates testable correlations between the (g-2) anomalies and LFV processes that were not present in previous realizations of the model. The authors start with the 3-4-1 gauge group and add a singly charged Higgs boson along with the inverse seesaw mechanism for neutrinos. They work out the one-loop contributions to the anomalous magnetic moments of the electron and muon, as well as to the LFV decays of the tau lepton, the SM-like Higgs, and the Z boson. A numerical scan over the allowed parameter space, respecting neutrino oscillation data and other experimental bounds, leads to the result that the current upper limit on the branching ratio for tau to mu gamma keeps any deviation in (g-2)mu within 10^{-9} of the Standard Model value at the 1 sigma level. Tighter future bounds on that LFV process would reduce the allowed deviation to 5 x 10^{-10}. This approach does well by explicitly contrasting the new correlations with those in earlier 3-4-1 studies and by providing quantitative limits that can guide experiments. The derivations follow standard loop calculations in extended models, and the stress test confirms there are no internal inconsistencies or missed constraints in the setup. The main soft spot is that the specific numbers come from a scan over free parameters, including Yukawa couplings in the inverse seesaw sector and masses of new Higgs and neutrino states. These can be tuned within ranges that satisfy the constraints, so the correlations are robust but the exact maximal deviations depend on the chosen parameter ranges. This is typical for such phenomenological papers and does not undermine the central claim. Readers who work on beyond-Standard-Model explanations for lepton anomalies or on 3-4-1 gauge extensions will find this paper relevant. It offers concrete predictions that distinguish the model from others. The paper demonstrates clear thinking through its detailed implementation and numerical analysis. It deserves a serious referee. I would recommend sending it to peer review rather than desk rejecting it.

Referee Report

0 major / 2 minor

Summary. The manuscript presents a 3-4-1 gauge extension with a singly charged Higgs boson and minimal inverse seesaw neutrinos. It derives one-loop contributions to the (g-2)e,μ anomalies and to LFV processes (τ→μγ, h→τμ, Z→τμ), then performs a numerical scan over the allowed parameter space subject to neutrino oscillation data and collider bounds. The central result is a set of strong correlations among these observables, with the current experimental upper limit on Br(τ→μγ) restricting the maximal (g-2)μ deviation to 10^{-9} within the 1σ experimental range, and future sensitivity tightening this to 5×10^{-10}.

Significance. If the numerical results hold, the work supplies concrete, falsifiable correlations between the (g-2) anomalies and LFV branching ratios that can be tested at Belle II and future colliders, distinguishing this 3-4-1 realization from earlier variants. Credit is due for the explicit one-loop expressions, the imposition of neutrino-mass and collider constraints, and the quantitative mapping of the allowed region in observable space.

minor comments (2)

[Section 3] Section 3 (or wherever the inverse-seesaw Yukawa matrices are introduced): explicit matrix forms for the Yukawa couplings and the small lepton-number-violating parameter would improve reproducibility of the loop integrals and mixing angles.
[Numerical results] Numerical scan subsection: the ranges, priors, and sampling method for the free parameters (Yukawas, new Higgs and neutrino masses) should be stated more precisely so that the reported maximal deviations and correlation bands can be independently verified.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript on LFV decays in the 3-4-1 model with minimal inverse seesaw neutrinos and for recommending minor revision. The referee summary correctly reflects the central predictions of strong correlations between the (g-2) anomalies and LFV rates, with the τ→μγ bound limiting the muon anomaly. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs a 3-4-1 gauge model with minimal inverse seesaw, derives one-loop contributions to (g-2)e,μ and LFV processes from explicit Feynman diagrams and mixing matrices, then performs a numerical scan over Yukawa couplings and mass parameters subject to neutrino oscillation data and collider bounds. The reported correlations and maximal (g-2)μ deviation under the Br(τ→μγ) limit emerge directly from evaluating the loop functions over the allowed parameter region; no step reduces by definition or self-citation to the target observables themselves. The central claim is therefore a genuine model prediction rather than a re-expression of fitted inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim depends on several fitted parameters in the scalar and fermion sectors to match the experimental anomalies, plus standard assumptions of the seesaw mechanism.

free parameters (2)

Yukawa couplings in inverse seesaw
Adjusted to fit (g-2) anomalies and LFV rates
Masses of new Higgs and neutrinos
Chosen to accommodate large (g-2) values while satisfying bounds

axioms (2)

domain assumption The 3-4-1 gauge symmetry and particle content
Standard extension assumed as the base model
domain assumption Minimal inverse seesaw mechanism generates small neutrino masses
Used to explain neutrino masses and contribute to anomalies

invented entities (1)

Singly charged Higgs boson no independent evidence
purpose: Mediates contributions to (g-2) and LFV decays
New particle postulated in the model to achieve the desired phenomenology

pith-pipeline@v0.9.0 · 5482 in / 1709 out tokens · 77410 ms · 2026-05-10T17:11:06.357173+00:00 · methodology

discussion (0)

Reference graph

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